Solve 4w^2 12w 9=169

Question

Solve the equation

w = \frac{3 676}{12}

Alternative Form

w \approx 0.731365

Evaluate

4 w^{2} \times 12 w \times 9 = 169

Multiply

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Evaluate

4 w^{2} \times 12 w \times 9

Multiply the terms

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Evaluate

4 \times 12 \times 9

Multiply the terms

48 \times 9

Multiply the numbers

432

432 w^{2} \times w

Multiply the terms with the same base by adding their exponents

432 w^{2 + 1}

Add the numbers

432 w^{3}

432 w^{3} = 169

Divide both sides

\frac{432 w ^{3}}{432} = \frac{169}{432}

Divide the numbers

w^{3} = \frac{169}{432}

Take the 3 -th root on both sides of the equation

3 w^{3} = 3 \frac{169}{432}

Calculate

w = 3 \frac{169}{432}

Solution

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Evaluate

3 \frac{169}{432}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 169}{3 432}

Simplify the radical expression

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Evaluate

3432

Write the expression as a product where the root of one of the factors can be evaluated

3 216 \times 2

Write the number in exponential form with the base of 6

3 6^{3} \times 2

The root of a product is equal to the product of the roots of each factor

3 6^{3} \times 32

Reduce the index of the radical and exponent with 3

632

\frac{3 169}{6 3 2}

Multiply by the Conjugate

\frac{3 169 \times 3 2 ^{2}}{6 3 2 \times 3 2 ^{2}}

Simplify

\frac{3 169 \times 3 4}{6 3 2 \times 3 2 ^{2}}

Multiply the numbers

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Evaluate

3169 \times 34

The product of roots with the same index is equal to the root of the product

3 169 \times 4

Calculate the product

3676

\frac{3 676}{6 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

632 \times 3 2^{2}

Multiply the terms

6 \times 2

Multiply the terms

12

\frac{3 676}{12}

w = \frac{3 676}{12}

Alternative Form

w \approx 0.731365

Show Solution